Clean the mushrooms, remove the stems and scrape out the black gills then slice the mushrooms into ¼ inch strips.
Add the mushrooms and chicken broth to a large non-stick skillet and cook over medium-high heat until the liquid evaporates, about 6 to 7 minutes.
Push the mushrooms to the edge of the pan and add the butter and oil. When the butter melts add the shallot, garlic, thyme, salt, and pepper and cook for 6 to 8 minutes to soften the shallots and brown the mushrooms.
Add the wine and cook for another 2 to 3 minutes to reduce the wine and cook the alcohol off.